University of Birmingham > Talks@bham > Theoretical computer science seminar > Adjunctions and Actions of Co/Cartesian Categories

Adjunctions and Actions of Co/Cartesian Categories

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When a category is cartesian it is possible to consider actions of such a monoidal structure in the sense of Janelidze and Kelly (2001). If F:X->A is adjoint to U:A->X, the latter will not only be cartesian but also give a linear transformation between canonical actions of X. In the dual situation where X and A are cocartesian, the adjoint F will not only be cocartesian but also a linear transformation of actions of A. If X and A are bicartesian, it turns out that there exists a module theoretic characterization of when F is adjoint to U. This fact is the generalization to categories of a result Jónsson and Tarski (1951) obtained for Galois connections between boolean operators, and which is fundamental in the axiomatization of relation algebras.

This talk is part of the Theoretical computer science seminar series.

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